C₁₉×#12593 #18018552

order	4864
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₉×#12593

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×#97
prime radical	C₂³×C₁₉	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

338 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,33,39,34,41,49,56,35,40,48,55,32,38,31,37)(30,42,45,58,46,36,43,52,47,54,50,51,44,53,59,57);(21,24)(25,27)(28,30)(29,36,40,53)(31,43)(32,44)(33,50)(34,46)(35,47)(37,51,56,58)(38,42,41,54)(39,57,55,52)(45,48)(49,59);(20,22,23,26)(21,25,24,27)(28,31,32,48,35,49,34,33)(29,37,38,55,40,56,41,39)(30,43,44,45,47,59,46,50)(36,51,42,52,53,58,54,57)

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5581);